The concept of pride in the Homeric epics differs somewhat from our modern understanding of pride.
The most famous Greek word for pride, hubris, indicates outrageous behavior that goes beyond the bounds of what is socially acceptable. So, if a host were to insult a guest or a guest were to insult a host, these would be an example of hubris. Paris was actually a guest in Menelaus' house when he abducted Helen. This would be an example of extreme hubris. In Homer's Odyssey, the Cyclops eats some of Odysseus' men. This is another example of extreme hubris.
Typically, examples of hubris involve human behavior that would be offensive to the gods (who frequently punish hubristic acts), so I would be quite interested to see if examples exist in which Homer explicitly describes the gods as engaging in acts of hubris.
In Iliad 5, when Ares battles against Athena, Athena might regard Ares' actions as hubristic. Likewise, in Iliad 21, when Artemis tries to battle against Hera, Hera seems to regard her actions as excessively prideful: "You shameless bitch, you dare stand against me?" (Ian Johnston translation)
Iliad 16 might provide an example in which Zeus is on the verge of engaging in an act of hubris as he considers violating what Fate has decreed and rescuing his son Sarpedon from death. We might also see an example of pride in the modern sense as Zeus calls his son "dearest of all men" (Ian Johnston translation). Here, Zeus contemplates an action that goes beyond the bounds of acceptable behavior. Accordingly, Hera tells Zeus that the other gods "will not all agree with you" (Ian Johnston translation).